Skip to main content

Measurement & Control - short answer type question from AMIE exams (Summer 2020)

Short answer type (2 x 4)

Find the dimension of Torque in the SI unit of the M, L, T, I system.

Dimension formula of torque = dimension formula of force X dimension formula of length

[MLT-2][L]=[ML2T-2]

Find the equivalent resistance of series connected two resistances R₁ = 40 ± 2% and R₂ = 60 ± 3%.

R1 + R2 = 40 ± 2 + 60 ± 3 = 100 ±5%

Write the type and order of a system whose transfer function is given by

G(s) = \frac{K}{{{s^2}(1 + sT)}}

Order of the system can be defined as the value of the highest exponent that appears in the denominator of the transfer function. (Total number of poles). In the given expression highest exponent is 3. Hence the order of the system is 3.

Find the no. of significant figures in 

(a) 0.0012

(b) 12.00

(c) 1200

(d) 12

0.0012 has 2 significant figures.

12.00 has 4 significant figures.

1200 has 2 significant figures. 

12 has 2 significant figures. 

Significant figures are the digits of a number that are meaningful in terms of accuracy or precision. They include:

  • Any non-zero digit
  • Zeros between non-zero digits as in 3003 or 45.60009
  • Trailing zeros only when there is a decimal point as in 6750. or 274.3300

Briefly explain the following (4 x 3)

Force voltage analogy

Consider the following figure.

Mechanical system

The element ‘mass’ in the mechanical system corresponds to an inductor in the electrical network.

F = M\frac{{d{x^2}}}{{dt}} = M\frac{{dv}}{{dt}}

where x represents the amount of displacement and v is the velocity.

Electrical network

V = L\frac{{di}}{{dt}}

Uses of Wien’s bridge method

Following are some of the important applications of the Wien bridge that are important from the subject point of view:

  • 1. This bridge is used for measuring the frequency in the audio range.
  • 2. The Wien bridge is used in audio and HF oscillators as the frequency-determining device.
  • 3. The bridge is used in a harmonic distortion analyser, as a notch filter, and an audio frequency and radio frequency oscillators as a frequency-determining element.

Absolute stability and relative stability

Relative stability

It is measure of how fast the transient dies out in the system .relative stability is related to settling time. a system having poles away from the left half of imaginary axis is considered to be relatively more stable compared to a system having poles closed to imaginary axis.

The relative stability may be found by shifting the imaginary axis to the left by some constant amount σ. This can be easily done by replacing s with s + σ in the characteristic equation and applying the Routh-Hurwitz criteria.

Absolute stability

If the system returns to its equilibrium state after the inputs given to the system are removed. Routh’s stability criterion provides information about absolute stability.

---
  • The study material for AMIE/B Tech/Junior Engineer exams is available at https://amiestudycircle.com
  • If you like the post please share your thoughts in the comment section 


Labels:

Comments

Post a Comment

Popular posts from this blog

Mechanics of Fluids (Solved Numerical Problems)

Numerical The surface Tension of water in contact with air at 20°C is 0.0725 N/m. The pressure inside a droplet of water is to be 0.02 N/cm² greater than the outside pressure. Calculate the diameter of the droplet of water. (7 marks) (AMIE Summer 2023) Solution Surface tension, σ = 0.0725 N/m Pressure intensity, P = 0.02 N/m 2 P = 4σ/d Hence, the Diameter of the dropd = 4 x 0.0725/200 = 1.45 mm Numerical Find the surface tension in a soap bubble of 40 mm diameter when the inside pressure is 2.5 N/m² above atmospheric pressure. (7 marks) (AMIE Summer 2023) Answer: 0.0125 N/m Numerical The pressure outside the droplet of water of diameter 0.04 mm is 10.32 N/cm² (atmospheric pressure). Calculate the pressure within the droplet if surface tension is given as 0.0725 N/m of water. (AMIE Summer 2023, 7 marks) Answer: 0.725 N/cm 2   Numerical An open lank contains water up to a depth of 2 m and above it an oil of specific gravity 0.9 for a depth of 1 m. Find the pressure intensity (i) at t...
Post a Comment
Read more

Energy Systems (Solved Numerical Problems)

Wind at 1 standard atmospheric pressure and \({15^0}C\) has velocity of 15 m/s, calculate (i) the total power density in the wind stream (ii) the maximum obtainable power density (iii) a reasonably obtainable power density (iv) total power (v) torque and axial thrust Given: turbine diameter = 120 m, and turbine operating speed = 40 rpm at maximum efficiency. Propeller type wind turbine is considered. (AMIE Winter 2023) Solution For air, the value of gas constant is R = 0.287 kJ/kg.K 1 atm = 1.01325 x 105 Pa Air density \(\rho  = \frac{P}{{RT}} = \frac{{1.01325x{{10}^5}}}{{287}}(288) = 1.226\,kg/{m^3}\) Total Power \({P_{total}} = \rho A{V_1}^3/2\) Power density \(\begin{array}{l}\frac{{{P_{total}}}}{A} = \frac{1}{2}\rho {V_1}^3\\ = \frac{1}{2}(1.226){(15)^3}\\ = 2068.87{\mkern 1mu} W/{m^2}\end{array}\) Maximum power density \(\begin{array}{l}\frac{{{P_{\max }}}}{A} = \frac{8}{{27}}\rho A{V^3}_1\\ = \frac{8}{{27}}(1.226){(15)^3}\\ = 1226{\mkern 1mu} W/{m^2}\end{array}\) Assuming eff...
Post a Comment
Read more

Design of Electrical Systems (Solved Numerical Problems)

Important note There is something wrong with this question paper. It seems that instead of "Design of Electrical Systems" the IEI has given problems from "Electrical Machines". You should raise a complaint to director_eea@ieindia.org in this regard. Numerical A 120 V DC shunt motor draws a current of 200A. The armature resistance is 0.02 ohms and the shunt field resistance is 30 ohms. Find back emf. If the lap wound armature has 90 slots with 4 conductors per slots, at what speed will the motor run when flux per pole is 0.04 Wb?​ (AMIE Summer 2023, 8 marks) Solution The back EMF (E b ) of a DC motor can be calculated using the formula: E b = V - I a R a   Given: V = 120 V I a = 200 A R a = 0.02 ohms Substituting the values into the formula: E b = 120 − 200 × 0.02 = 120 − 4​ = 116 V Now, let's calculate the speed (N) at which the motor will run using the given flux per pole (φ p ). The formula to calculate the speed of a DC motor is: N = 60×E b /(P×φ p ) Wh...
Post a Comment
Read more